A performer, seated on a trapeze, is swinging back and forth with a period of 9.55 s. If she stands up, thus raising the center of mass of the trapeze + performer system by 20.0 cm, what will be the new period of the system? Treat trapeze + performer as a simple pendulum.
(a) ____ s
..this is what i did:
T = 2pi sqrt(2L/3g)
1.64 s = 2pi sqrt(((2)(Xm))/((3)(9.8m/s^2)))
[[rearranged to solve for Xm]]
Xm = (((1.64s/2pi)^2)((3)(9.8m/s^2)))/(2)
Xm = 3307.99 m
[[the center of mass increased 20.0cm]]
Xm2 = 3307.99 m + 0.2 m
Xm2 = 3308.19 m
[[plug into original equation]]
T = 2pi sqrt(2L/3g)
T = 2pi sqrt(((2)(3308.19m))/((3)(9.8m/s^2)))
T = 94.3 s
[[final answer]]
.. did i do it right? .. if not, what am i missing or do wrong? thanks!
No, you did not do it right. The work makes no sense to me.
From T=2PI sqrt (l/g), solve for l in the original equaiton. Your work above is similar, but the wrong equation (where did 2/3 come from, and 1.64?
Now, knowing the length l, add twenty cm. Refigure the period.
Wouldn't you have a clue when you found the length of the pendulum as 3308meters long? That is not reasonable.
To solve this problem, we can use the equation for the period of a simple pendulum, which is given by:
T = 2π√(L/g)
Where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity (approximately 9.8 m/s²).
In the given problem, we are told that the performer raises the center of mass of the trapeze + performer system by 20.0 cm. This means that the new length of the pendulum, L, will be equal to the original length plus the additional 20.0 cm.
So, the new equation for the period becomes:
T' = 2π√((L + ΔL)/g)
Where T' is the new period, ΔL is the change in length of the pendulum (20.0 cm), and g is the acceleration due to gravity.
To find the new period, we can substitute the values into the equation:
T' = 2π√((L + 0.2 m)/9.8 m/s²)
Now, we just need to calculate the value of L. We are not given the original length in the problem statement, so we cannot directly find L. It seems that there might be some confusion in your initial work.
I apologize for the misunderstanding. Can you clarify if any additional information is given in the problem statement that provides the original length of the trapeze + performer system? This information is necessary to correctly solve the problem.